1.3 Show that the following equation represents a sphere, and find its center and radius. x? +y? + z? – 6x + 8y – 10z + 25 = 0

Q: Consider the hypergeometric equationx(1−x)y′′+[c−(a+b+1)x]y′−aby = 0,…

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Q: 7. Identify the surface for each of the following equations. (a) z = r² (b) r² + z² = rl (c) p = 4…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Identify the equation associated with each graphed surface. (a) O 22 = - x? – y? + 1 O22 – 1 = y + x…

A: Given graph is  (a)                                                      from graph we observe that…

Q: 7. Identify the surface for each of the following equations. (a) z = r? (b) r² + z² = r' (c) p= 4…

A: We to identify the surface for each of the following equations  a z = r2      consider x = r cosθ, y…

Q: WfSTC of the following statements are true? I. y = -x³ + 3x is symmetric to the origin. II. If f(x)…

A: To define given statement s are true or not

Q: 2. Find the equation of the sphere with the given conditions: (a) center at (1, – 2, – 4) and its…

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Q: a) Find the center of the sphere satisfying the equation, x2 + y2 + z2 - 2x + 4y + 2z = 10.…

A: The given equation of sphere,   x2+y2+z2-2x+4y+2z=10

Q: %3D at

A: We need to substitute  x=au ,y = bv ,z= cw

Q: 6. State the center and radius of the circle: x + y² – 4x + 2y = 16 Center: (-2, 1) and r = 21…

A: The solution as follows :-

Q: Question 9 Which surface has the following equation? a2-2y = 32 O Cylinder O Plane O Paraboloid O…

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Q: Find the standard equation of the sphere with the given characteristi Center: (-1, -9, 7) Radius: 9…

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Q: Which of the following is not a parametrization of the parabola y = r² ? Oz= Vt, y=t Oz-t, y-t Oz- ,…

A: We will check which parametrisation is correct.

Q: Sketch the section of the surface at x = 0. y? - 25z? = 25 12 -12 -8 12 -4 -8 -12 4 -6 -2 -4 4.

A: topic - hyperbola

Q: Find the distance between the point (p, 4p) and the parabola y? = 2px, where p is a fixed positive…

A: let the point on parabola be A= (x, y)  B = (p, 4p) Thus,  AB = x-p2+y-4p2 but parabola is y2=2px…

Q: sketch the given surface. x 2+ 9y 2 + 4z 2 = 36

A: To sketch the given graph

Q: Find the area of each of the following surfaces.   The portion of the sphere with equation x 2+y 2+z…

A: Given, x2+y2+z2=16 , lies inside  x2+y2=9 surface area =2∬1+zx2+zy2dxdy…

Q: Which of the following is the equation of a sphere with radius r = (-1,0,-2)? Select one: O None of…

A: This question is related to equation of sphere, we will solve it using given information.

Q: 10. Identify the surface that is given by: p (sin? (6) cos (0) + cos ()) = 4

A: (10) Consider the given expression as shown below:

Q: Find the center and radius of each sphere. Sphere: x? + y? + z² – 10x - 8y + 6z = 0 Center: Radius:…

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Q: 3) A surface M is enc where e, = 6 luivldu on this surface. d)Find the Gauss cu

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Q: 2 Find the cartesiun equation for the polar Carre rこlcos . Al(x-2)²+y2=4 ty²-4 %3D c)x²+ Cy-2)?=4 D)…

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Q: Identify the surface 2x² + 4y? – 1=0. A. An elliptic cylinder. B.Ahyperbolic cylinder. OC. None of…

A: We will solve the problem

Q: Part 4 of 8 Since we want the portion of the sphere which is above this circle, we return to the…

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Q: The equation x² – 2x + y - 4y + z2 – 2z – 10 = 0 | | represents the equation of a sphere centered at…

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Q: Question 11 Calculate the surface area of the given surface. The parabolic cylinder with equation z…

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Q: Answer the following questions about the sphere whose equation is given by 2+7 +2 - 8z + 6y = 75. 1.…

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Q: 3. Fit a second degree parabola y = ax? + bx + c to the following data %3D 3. 4 y 1 1.8 1.3 2.5 6.3…

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Q: on the hyperbola xy = 1. %3D Which of the followings is TRUE for f(x, y) = x² + y? %3D Litfen birini…

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Q: Identify the surface in Cartesian coordinate for each of the following equations. a) p=5 and b)…

A: Given equations are in polar coordinates and we have to write their equation in Cartesian…

Q: Identify the surface in the xyz coordinate system given by the equation: z=-√(4-y^2) O cylinder O…

A: Let's find.

Q: 3. Consider the equation for a sphere Si given by 2x2 + 16x + 2y? – 18y + 22 = 20z – 22 (a) Find the…

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Q: Answer the following questions about the sphere whose equation is given by 2² + y? + 2? – 6z + 4y =…

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Q: Identify the equation associated with each graphed surface. (a) O z? – 1 = y? + 2? O 22 + y² = z O…

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Q: Find a spherical coordinate equation for the sphere x² + y? + (z – 1)? =1 Select one: а. p = 3cos Ø…

A: Let us consider rectangular coordinates x,y,z and spherical coordinates ρ,θ,φ. Equations which…

Q: Assume you are given the surface S with equation ? 9 1. 4 O Find the equation of the tangent plane…

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Q: (a) x² + 2x + 4y² + 16y + 9z? 19

A: Sketch and identify the surfaces: (a) x2+2x+4y2+16y+9z2=19.

Q: 8. Show that the circle and the ellipse are tangent to each other and draw the figure, x? + y? – 6x…

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Q: 9. The Whitney umbrella surface is given parametrically by I= uv, y = v, 2= u. A picture of this…

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Q: 3. Evaluate ff, (x² + y²)³/²dA, where D is the region in the first quadrant bounded by the x-axis,…

A: Given problem:- Evaluate ∫∫D (x² + y²)3/2 dA, where D is the region in the first quadrant bounded by…

Q: 2) The (Beltrami) pseudosphere is given by the chart x(uivl = (coslu) SinCv), Sincul Sincv), coscv)+…

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Q: Evaluate x° ds where C is the part of the parabola y = x² from (0,0) to (2, 4).

A: Form the double integral and set the limits than integrate with respect to y and x.

Q: Evaluate (x - iy) dz along (a) the parabola y = 2r? from (1, 2) to (2, 8),

A: In the given problem we have to evaluate  ∫C(x2-iy2)dz  along the parabola  y=2x2 from (1,2) to (2,…

Q: Write the sphere in standard form. x + y + z? 6x + 2y – 2z = 14

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Q: 8. Suppose the earth is a sphere with equation r2 + y? + 22 1. On this earth, Edmonton has…

A: Draw the diagram of the condition given. Now the point from which both the stations are visible is…

Q: Find a spherical coordinate equation for the sphere x²+y? +(z- 1)? = 1 Select one: a. P= cos Ø O b.…

A: All real numbers can be represented on a line called the number line. The number zero corresponds to…

Q: Find parametric equations for the following curves in R³. (a) The great circle on the sphere x² + y²…

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Q: T 1) Reflect quadrilateral ABCD across the y-ar reflection on the coordinate plane to the right. new…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Which of the following conditions will make the (yーk)? (xーh)? equation a2 (z-1)? = 1 an equation of…

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Q: 10. Given the expression x* – 3x + 7 = y* on the interval [3,5], determine the surface of revolution…

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